Question

The mean of 100 observations is $50$ and their standard deviation is $5$. The sum of the squares of all the observations is

• A. $50000$
• B. $250000$
• C. $252500$
• D. $255000$

Answer 1

Answer: (C)

$252500$

We know, Standard deviation, ${\sigma }^2=\frac{\sum x^2}{n}-{\left(\overline{x}\right)}^2$
Given, $\sigma =5,\sum x=50,n=100$
$\Rightarrow 25=\frac{\sum x^2}{100}-{\left(50\right)}^2$
$\Rightarrow \sum x^2=252500$
Thus sum of squares of all the observation is 252500.